Spin Decomposition of Electron in QED

TL;DR

This paper systematically analyzes the electron spin decomposition in QED at one-loop order, confirming the equivalence of different angular momentum definitions and clarifying issues related to light-front quantization and potential angular momentum.

Contribution

It provides a detailed comparison of spin decomposition schemes in QED, demonstrating their agreement and resolving recent ambiguities in light-front approaches.

Findings

Electron orbital angular momentum definitions agree at one-loop order.

Potential angular momentum vanishes at this order.

Identifies missing contributions in light-front quantization.

Abstract

We perform a systematic study on the spin decomposition of an electron in QED at one-loop order. It is found that the electron orbital angular momentum defined in Jaffe-Manohar and Ji spin sum rules agrees with each other, and the so-called potential angular momentum vanishes at this order. The calculations are performed in both dimensional regularization and Pauli-Villars regularization for the ultraviolet divergences, and they lead to consistent results. We further investigate the calculations in terms of light-front wave functions, and find a missing contribution from the instantaneous interaction in light-front quantization. This clarifies the confusing issues raised recently in the literature on the spin decomposition of an electron, and will help to consolidate the spin physics program for nucleons in QCD.